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A Formula for the Multiplicity of a Weight

In: Collected Papers

Author

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  • Bertram Kostant

    (Massachusetts Institute of Technology, Department of Mathematics)

Abstract

Let g be a complex semi-simple Lie algebra and h a Cartan subalgebra of g. Let ?? be an irreducible representation of g, with highest weight ?, on a finite dimensional vector space V ?. A well known theorem of E. Cartan asserts that the highest weight, ?, of ?? occurs with multiplicity one. It has been a question of long standing to determine, more generally, the multiplicity of an arbitrary weight of ??. Weyl’s formula (1.12) for the character of ?? is an expression for the function ??(?) = tr exp ??(?), ??h, on h in terms of ? and quantities independent of the representation.

Suggested Citation

  • Bertram Kostant, 2009. "A Formula for the Multiplicity of a Weight," Springer Books, in: Anthony Joseph & Shrawan Kumar & Michèle Vergne (ed.), Collected Papers, pages 109-129, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-09583-7_10
    DOI: 10.1007/b94535_10
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